Question

the area of a rectangular wall of a barn is 91 square feet. its length is 6 feet longer than the width. find the length and width of the wall of the barn. the width is 7 feet. the length is feet.

Explanation:

Step1: Define variables

Let the width be $w$ and length be $l$. Given $l = w + 6$ and area $A=l\times w = 91$.

Step2: Substitute length formula into area formula

$(w + 6)\times w=91$, which expands to $w^{2}+6w - 91 = 0$.

Step3: Solve quadratic equation

Factor the quadratic: $(w + 13)(w - 7)=0$. So $w=- 13$ or $w = 7$. Since width can't be negative, $w = 7$.

Step4: Find the length

Since $l=w + 6$ and $w = 7$, then $l=7 + 6=13$.

Answer:

13